Yikes. Sounds like either misinterpretation or really bad advice.
Whether or not funds are remitted to the US has never played ANY role in whether or not it is reportable or taxable. Never.
You can take a tax credit for the taxes already paid on the income, or it could possibly be subject to a treaty provision if the income is from a country with which the US has a treaty for that type of income, but not reporting it isn't generally an option in either of these scenarios. You either report it for a credit or you report it and assert your treaty position.
